A product with an annual demand of 1000 units has EOQ (Economic Order Quantity)

Question

A product with an annual demand of 1000 units has EOQ (Economic Order Quantity) = 80. The demand during the lead time follows a normal probability distribution with µ = 25 and =5 during the reorder period.

a. How much safety stock is required, if the firm desires at most a 2% probability of a stockout on any given order cycle?

b. If a manager sets the reorder point at 30, what is the probability of a stockout on any given order cycle? How many times would you expect to stockout during the year, if this reorder points were used?

Explanation / Answer

Solution:

a) Safety stock = Zcritical * +
= -2.055 *5 +25
= 14.725
b) P(x < 30) = P(Z < 30-25/5)
= P(Z < 1)
= 0.8413
Expected number of times = 80*0.8413 = 67 times

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